Certainly! Let's solve the problem step-by-step.
### Step 1: Determine the rate of pumping gas in gallons per minute.
The motorist is pumping gas into his car at a rate of [tex]\(\frac{5}{12}\)[/tex] of a gallon every [tex]\(\frac{1}{24}\)[/tex] of a minute. First, we need to find the rate in terms of gallons per minute.
To do this, we can divide the amount of gas pumped by the time taken:
[tex]\[
\text{Rate} = \frac{\frac{5}{12} \text{ gallons}}{\frac{1}{24} \text{ minutes}}
\][/tex]
When dividing fractions, we multiply by the reciprocal:
[tex]\[
\text{Rate} = \frac{5}{12} \div \frac{1}{24} = \frac{5}{12} \times \frac{24}{1} = \frac{5 \times 24}{12 \times 1} = \frac{120}{12} = 10 \text{ gallons per minute}
\][/tex]
### Step 2: Calculate the amount of gas pumped in [tex]\(\frac{1}{2}\)[/tex] of a minute.
Now, we need to find out how many gallons of gas are pumped in [tex]\(\frac{1}{2}\)[/tex] of a minute given the rate of 10 gallons per minute.
We use the formula:
[tex]\[
\text{Amount of gas pumped} = \text{Rate} \times \text{Time}
\][/tex]
Given the rate is 10 gallons per minute and the time is [tex]\(\frac{1}{2}\)[/tex] minute, we have:
[tex]\[
\text{Amount of gas pumped} = 10 \text{ gallons per minute} \times \frac{1}{2} \text{ minute} = 10 \times 0.5 = 5 \text{ gallons}
\][/tex]
### Conclusion:
The motorist will have pumped 5 gallons of gas into his car in [tex]\(\frac{1}{2}\)[/tex] of a minute.
So, the correct answer is:
[tex]\[
\boxed{5}
\][/tex]
